After months of using his bully pulpit to pressure Republicans — a strategy that one White House ally has described as putting his opponents in between "Barack and a hard place" — President Obama has reportedly invited a handful of moderate GOP lawmakers to dinner on Wednesday night in a bid to reach a "grand bargain" to reduce the budget deficit. The olive branch comes less than a week after Congress failed to reach a deal to replace the so-called sequester, allowing $85 billion in painful, across-the-board spending cuts to begin taking effect. The administration still has hopes that it can enact a balanced deficit-reduction program that includes new tax revenues and cuts to entitlement programs — but will Republicans go along?

So far, some Republicans appear to be taking Obama's overtures seriously, according to Jackie Calmes and Jonathan Weisman at The New York Times:

"Maybe because of sequestration and frustration with the public, the time is right to act, and what I see from the president is probably the most encouraging engagement on a big issue since the early days of his presidency," said Senator Lindsey Graham, Republican of South Carolina, who received a call from Mr. Obama on Tuesday.

Speaking of the deficit reduction impasse, Mr. Graham added, "He wants to do the big deal." [The New York Times]

Graham has publicly said he is open to raising $600 billion in revenue by closing tax loopholes, which is in line with the administration's proposals, as long as entitlement programs like Medicare and Social Security, which make up the lion's share of the deficit, are on the table. That stands in stark contest to the position of House Speaker John Boehner (R-Ohio) and Senate Minority Leader Mitch McConnell (R-Ky.), both of whom have rejected any new tax revenue. According to Democratic analysts, some Senate Republicans are not only keen on reaching a policy goal of reducing entitlement spending, but reaping political rewards, says Politico:

While the White House is still intent on hammering House Republicans they view as unreachable, Obama increasingly sees a path out of gridlock through the Senate GOP conference, whose members want to prove their party is capable of big, meaningful bipartisan deals that belie the "Party of No" label. [Politico]

It's certainly true that Obama is handing Republicans a golden opportunity to cut entitlements, while providing them with political cover. "The key," writes Scott Galupo at The American Conservative, "will be how wisely Republicans use their leverage: Will they get something in return for it, or will they bludgeon themselves with the lever?"

However, many are understandably skeptical that the two sides can reach an agreement, since it would likely anger the Republican base. As Steve Benen at The Maddow Blog notes:

Boehner and McConnell aren't refusing to govern, compromise, or work in good faith because they're stubborn; they're refusing because they represent the will of their respective caucuses. By all accounts, the House Speaker likely would have accepted any number of compromise offers from the White House over the last couple of years — if only Boehner had any confidence his own members would be willing to follow his lead.

Similarly, even some of the GOP lawmakers the president has begun chatting up aren't ignoring fair offers solely because they're intransigent; they're also ignoring fair offers because they know working constructively with a Democratic president will lead to primary challenges they may very well lose. [MSNBC]

Indeed, some liberals think Obama is rewarding Republicans for their unwillingness to compromise. All Obama is doing, writes Brian Beutler at Talking Points Memo, "is acquiescing to the unchanging nature of the Republican Party."

At the very least, Obama's outreach could put to bed the idea that he hasn't offered any entitlement cuts, a common, erroneous theme of Republican complaints in the days running up to the sequester. That would help if Obama were ever to return to his "Barack and a hard place" strategy.